Knot complement

Complement of a knot in three-sphere

In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is the 3-sphere minus the space near the knot. To make this precise, suppose that K is a knot in a three-manifold M. Let N be a tubular neighborhood of K; so N is a solid torus. The knot complement is then the complement of N,

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